Harnack inequality and self-similar solutions for fully nonlinear fractional parabolic equations

被引：0
作者：
Gonzalo Dávila
Alexander Quaas
Erwin Topp
机构：
[1] Universidad Técnica Federico Santa María,Departamento de Matemática
[2] Universidad de Santiago de Chile,Departamento de Matemática y C.C.
来源：
Calculus of Variations and Partial Differential Equations | 2023年 / 62卷
关键词：
35K55; 35D40; 35A08;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We find bounds for the principal eigenvalue and eigenfunction associated to the existence of self-similar solutions to a fully nonlinear parabolic problem. In contrast with the local case, the upper and lower bounds for the eigenfunction are of the same polynomial order |x|-(N+2s)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|x|^{-(N+2s)}$$\end{document}. In order to accomplish this we prove a Harnack inequality for general nonlocal elliptic equations with zero order terms.
引用
收藏
相关论文
共 49 条
  • [11] Kassmann M(2014)Nonlinear equations for fractional Laplacians, I: regularity, maximum principles, and Hamiltonian estimates Ann. Inst. H. Poincare Anal. Non Lineaire 32 1245-1260
  • [12] Bass RF(2007)An extension problem related to the fractional Laplacian Commun. Partial Differ. Equ. 62 597-638
  • [13] Levin DA(2009)Regularity theory For nonlocal integro-differential equations Commun. Pure Appl. Math. 29 833-859
  • [14] Berestycki H(2012)Regularity for solutions of non local, non symmetric equations Ann. Inst. H. Poincaé Anal. Non Linéaire 266 5971-5997
  • [15] Nirenberg L(2016)Continuous viscosity solutions for nonlocal Dirichlet problems with coercive gradient terms Math. Ann. 7 77-116
  • [16] Varadhan S(2019)Existence, nonexistence and multiplicity results for fully nonlinear nonlocal Dirichlet problems J. Differ. Equ. 226 2712-2738
  • [17] Berestycki H(1982)The local regularity of solutions of degenerate elliptic equations Commun. Partial Differ. Equ. 376 514-527
  • [18] Hamel F(2011)Fundamental solutions and Liouville type theorems for nonlinear integral operators Adv. Math. 54 3571-983
  • [19] Rossi L(2011)Fujita type exponent for fully nonlinear parabolic equations and existence results J. Math. Anal. Appl. 31 975-undefined
  • [20] Blumenthal RM(2015) regularity for concave nonlocal fully nonlinear elliptic equations with rough kernels Calc. Var. undefined undefined-undefined
12345